[opendtv] Re: Precision

I have never properly understood filtering of analog signals or become competent at all the EE math. So I usually prefer to just visualize signals as they appear as a discrete set of measurements (say voltage over time) in the digital domain.
But if you have a finite limited set of samples you can run the math, say Fourier transforms, and calculate a set of amplitudes of sin and cosine waves that would fit those measurements.
The problem is, that calculation will not come up with a unique answer since there are always sets of higher frequencies that would also pass through those same points, fitting those measurements and produce the same answers. Those are aliases. They create further problems because, while they happily pass through all the same sample points, they will in general not give the same predictions if you also use them to interpolate BETWEEN the original points. This causes problems for slowly moving objects and motion compensation both in codecs and in the human visual system.
It is one of the reasons deinterlacing works poorly. Either you filter vertically to nyquist and thus have reliable resolutions that can be predicted mostly by a simple bobbing algorithm or you try (typically) for greater than nyquist resolutions which are ALWAYS encoded with the potential ambiguity of aliasing and are thus guaranteed to NOT be correctly predictable in all cases. 

- Tom

Albert Manfredi wrote:

Al Limberg wrote:


"Aliasing" is used to describe what happens in digital video
when it is sampled at a rate less than twice its highest
frequency.  The undersampling of the high frequencies
creates spurious low-frequency components.  The
phemenon is sometimes referred to as "frequency-spectrum
folding".



In general, in any sampled waveform.
On a spectrum analyzer, a waveform sampled at regular intervals in the time domain looks like a series of identical frequency spectra in the frequency domain, recurring at n*sampling frequency, for any integer n from - infinity to + infinity. (That's why the D/A converter needs a final low-pass filter. Need to get rid of all those other spectra, which would otherwise become high frequency noise.)
If you fiddle with the initial low-pass filter in the A/D converter, or with the sampling frequency, you can see the train of identical frequency spectra come closer together or move further apart. If you tune the system so that the sampling frequency is less than twice the max signal frequency, the train of identical frequency spectra will begin to overlap over one another.
I think that's what "aliasing" means. You see an alias of the frequency spectrum intruding into the baseband signal frequency spectrum you're interested in. Frequency spectrum folding describes the same phenomenon.
Oversampling in the A/D or the D/A conversion process is a trick to move the frequency spectra further apart than they otherwise would have been. Its purpose is to to make the initial and/or final low-pass filters less critical. Don't need to be as steep to remove the other spectra, so they have less of an opportunity to distort the original signal. 

Bert

_________________________________________________________________
Like the way Microsoft Office Outlook works? You’ll love Windows Live Hotmail. http://imagine-windowslive.com/hotmail/?locale=en-us&ocid=TXT_TAGHM_migration_HM_mini_outlook_0507 



----------------------------------------------------------------------
You can UNSUBSCRIBE from the OpenDTV list in two ways:
- Using the UNSUBSCRIBE command in your user configuration settings at FreeLists.org - By sending a message to: opendtv-request@xxxxxxxxxxxxx with the word unsubscribe in the subject line. 




--
Tom Barry                  trbarry@xxxxxxxxxxx  




----------------------------------------------------------------------
You can UNSUBSCRIBE from the OpenDTV list in two ways:
- Using the UNSUBSCRIBE command in your user configuration settings at FreeLists.org 
- By sending a message to: opendtv-request@xxxxxxxxxxxxx with the word 
unsubscribe in the subject line.

Other related posts: